Hamiltonian Mechanical Systems and Geometric Quantization [electronic resource] /

1 Symplectic Geometry -- 1.1 Symplectic Algebra -- 1.2 Symplectic Geometry -- 1.3 Darboux’s Theorem -- 1.4 Symplectic Reduction -- 1.5 Problems and Solutions -- 2 Hamiltonian Mechanics -- 2.1 Hamiltonian Mechanical Systems -- 2.2 Poisson Bracket -- 2.3 Infinite Dimensional Hamiltonian Mechanical Systems -- 2.4 Problems and Solutions -- 3 Lie Groups. Momentum Mappings. Reduction -- 3.1 Lie Groups -- 3.2 Actions of Lie Groups -- 3.3 The Momentum Mapping -- 3.4 Reduction of Symplectic Manifolds -- 3.5 Problems and Solutions -- 4 Hamilton-Poisson Mechanics -- 4.1 Poisson Geometry -- 4.2 The Lie-Poisson Structure -- 4.3 Hamilton-Poisson Mechanical Systems -- 4.4 Reduction of Poisson Manifolds -- 4.5 Problems and Solutions -- 5 Hamiltonian Mechanical Systems and Stability -- 5.1 The Meaning of Stability -- 5.2 Hamilton’s Equations and Stability -- 5.3 The Energy-Casimir Method -- 5.4 Problems and Solutions -- 6 Geometric Prequantization -- 6.1 Full Quantization and Dirac Problem -- 6.2 Complex Bundles and the Dirac Problem -- 6.3 Geometric Prequantization -- 6.4 Problems and Solutions -- 7 Geometric Quantization -- 7.1 Polarizations and the First Attempts to Quantization -- 7.2 Half-Forms Correction of Geometric Quantization -- 7.3 The Non-Existence Problem -- 7.4 Problems and Solutions -- 8 Foliated Cohomology and Geometric Quantization -- 8.1 Real Foliations and Differential Forms -- 8.2 Complex Foliations and Differential Forms -- 8.3 Complex Elliptic Foliations and Spectral Geometry -- 8.4 Cohomological Correction of Geometric Quantization -- 8.5 Problems and Solutions -- 9 Symplectic Reduction. Geometric Quantization. Constrained Mechanical Systems -- 9.1 Symplectic Reduction and Geometric Prequantization -- 9.2 Symplectic Reduction and Geometric Quantization -- 9.3 Applications to Constrained Mechanical Systems -- 9.4 Problems and Solutions -- 10 Poisson Manifolds and Geometric Prequantization -- 10.1 Groupoids -- 10.2 Symplectic Groupoids -- 10.3 Geometric Prequantization of Poisson Manifolds -- 10.4 Problems and Solutions -- References.

Bibliographic Details

Main Authors:	Puta, Mircea. author., SpringerLink (Online service)
Format:	Texto biblioteca
Language:	eng
Published:	Dordrecht : Springer Netherlands : Imprint: Springer, 1993
Subjects:	Mathematics., Global analysis (Mathematics)., Manifolds (Mathematics)., Applied mathematics., Engineering mathematics., Differential geometry., Quantum physics., Global Analysis and Analysis on Manifolds., Applications of Mathematics., Quantum Physics., Differential Geometry.,
Online Access:	http://dx.doi.org/10.1007/978-94-011-1992-4
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